Lisa's response to me was a reply-all, so everyone who I invited could see that she was bringing her boyfriend. Since I didn't want everyone else to get confused, I hit reply-all as well. It took a while but Lisa did respond: "Oh sorry! I didn't know. Ya that's totally fine." So I guess it was okay after all.
I wish I had thought of the responses you guys came up with. Somehow just seems to flow better and seems more polite than what I came up with. Still, Lisa is generally a very sweet person and doesn't tend to care whether her boyfriend comes with or not so hopefully, she did not take offense.
BTW, the nudist thing made me laugh out loud.